Quantum anholonomies in time-dependent Aharonov-Bohm rings

Tanaka, Atushi; Cheon, Taksu

doi:10.1103/physreva.82.022104

Cited by 7 publications

(10 citation statements)

References 23 publications

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“…The effect reveals that the electromagnetic potentials, rather than the electric and magnetic fields, are the fundamental quantities in quantum mechanics. The interest in this issue appears in the different contexts, such as solid-state physics [3], cosmic strings [4][5][6][7][8][9][10][11][12][13][14] κ-Poincaré-Hopf algebra [15,16], δ-like singularities [17][18][19], supersymmetry [20,21], condensed matter [22,23], Lorentz symmetry violation [24], quantum chromodynamics [25], general relativity [26], nanophysics [27], quantum ring [28][29][30], black hole [31,32] and noncommutative theories [33,34].…”

Section: Introductionmentioning

confidence: 99%

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

2013

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In this work the bound state and scattering problems for a spin-1/2 particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a δ-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and S matrix are determined in terms of the self-adjoint extension parameter, which is explicitly determined in terms of the parameters of the problem. The relation between the bound state and zero modes and the failure of helicity conservation in the scattering problem and its relation with the gyromagnetic ratio g are discussed. Also, as an application, we consider the spin-1/2 Aharonov-Bohm problem in conical space plus a two-dimensional isotropic harmonic oscillator.The Aharonov-Bohm (AB) effect [1] (first predicted by Ehrenberg and Siday [2]) is one of most weird results of quantum phenomena. The effect reveals that the electromagnetic potentials, rather than the electric and magnetic fields, are the fundamental quantities in quantum mechanics. The interest in this issue appears in the different contexts, such as solid-state physics [3], cosmic strings [4][5][6][7][8][9][10][11][12][13][14] κ-Poincaré-Hopf algebra [15, 16], δ-like singularities [17-19], supersymmetry [20, 21], condensed matter [22, 23], Lorentz symmetry violation [24], quantum chromodynamics [25], general relativity [26], nanophysics [27], quantum ring [28-30], black hole [31, 32] and noncommutative theories [33, 34].In the AB effect of spin-1/2 particles [7], besides the interaction with the magnetic potential, an additional two dimensional δ-function appears as the mathematical description of the Zeeman interaction between the spin and the magnetic flux tube [18,19]. This interaction is the basis of the spin-orbit coupling, which causes a splitting on the energy spectrum of atoms depending on the spin state. In Ref. [17] is argued that this δ-function contribution to the potential can not be neglected when the system has spin, having shown that changes in the amplitude and scattering cross section are implied in this case. The presence of a δ-function potential singularity, turns the problem more complicated to be solved. Such kind of point interaction potential can then be addressed by the self-adjoint extension approach [35]. The self-adjoint extension of symmetric operators [36] is a very powerful mathematical method and it can be applied to various systems in relativistic and nonrelativistic quantum mechanics, supersymmetric quantum mechanics and vortex-like models.This paper extends our previous report [37] on a general physical regularization method, both in details and depth. The method has the advantage of solving problems in relativistic and nonrelativistic quantum mechanics whose Hamiltonian is s...

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Section: Introductionmentioning

confidence: 99%

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

2013

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“…Equation ( 24) describes the quantum dynamics of vector bosons in the presence of the Aharonov-Bohm potential. From (24) we can see that scattering states occur only if k ∈ R, whereas bound states occur only if k = i|k|.…”

Section: Aharonov-bohm Problem For the Spin-1 Sectormentioning

confidence: 99%

Relativistic quantum dynamics of vector bosons in an Aharonov–Bohm potential

Castro¹,

Silva²

2017

J. Phys. A: Math. Theor.

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The Aharonov-Bohm (AB) problem for vector bosons by the Duffin-Kemmer-Petiau (DKP) formalism is analyzed. Depending on the values of the spin projection, the relevant eigenvalue equation coming from the DKP formalism reveals an equivalence to the spin-1/2 AB problem. By using the self-adjoint extension approach, we examine the bound state scenario. The energy spectra are explicitly computed as well as their dependencies on the magnetic flux parameter and also the conditions for the occurrence of bound states.PACS 04.62.+v · 04.20.Jb · 03.65.Pm · 03.65.Ge

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“…Note that the following argument is also applicable to the case ω = 2πr/d with an integer 0 r < d. We assume that |v satisfies Eq. (9). This allows us to introduce a mapping of the kicked top into a kicked particle in a periodic lattice (or, a kicked tight-binding model).…”

Section: Explicit Expressions Of Eigenvalues and Eigenvectorsmentioning

confidence: 99%

“…Namely, under the presence of such an exotic quantum holonomy, the initial and final states of an adiabatic cycle belong to different eigenspaces. The exotic quantum holonomy has been studied both in one-body [5][6][7][8][9][10] and in many-body systems [11]. Applications of the exotic quantum holonomy to quantum state manipulation and adiabatic quantum computation [12] were also proposed [5,6,13].…”

Section: Introductionmentioning

confidence: 99%

Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops

2014

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The correspondence between exotic quantum holonomy, which occurs in families of Hermitian cycles, and exceptional points (EPs) for non-Hermitian quantum theory is examined in quantum kicked tops. Under a suitable condition, an explicit expression of the adiabatic parameter dependencies of quasienergies and stationary states, which exhibit anholonomies, is obtained. It is also shown that the quantum kicked tops with the complexified adiabatic parameter have a higher-order EP, which is broken into lower-order EPs with the application of small perturbations. The stability of exotic holonomy against such bifurcation is demonstrated.

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Quantum anholonomies in time-dependent Aharonov-Bohm rings

Cited by 7 publications

References 23 publications

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

Relativistic quantum dynamics of vector bosons in an Aharonov–Bohm potential

Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops

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